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Category Archives: statistics

Economists demonstrate exactly why bank robbery is a bad idea

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In most papers we at Ars cover, we'll be pleasantly surprised to find a single clever turn of phrase that has survived multiple rounds of editing and peer review. So it was an unexpected surprise to come across a paper where the authors, all professors of economics, have spent the entire text with tongues so firmly planted in their cheeks that they threatened to burst out, alien-style. It surprised me even more to find it in a journal that is produced on behalf of the Royal Statistical Society and American Statistical Association. Credit to the statisticians, though, for the journal's clever name: Significance.

What topic allowed the economists to cut loose? Bank robberies—or more specifically, the finances thereof. The UK's banking trade organization decided it wanted an analysis of the economic effectiveness of adding security measures to bank branches. The professors did that, but in the process, they also did an analysis that looked at the economics of bank robbery from the thieves' perspective.

The results were not pretty. For guidance on the appropriateness of knocking over a bank, the authors first suggest that a would-be robber might check with a vicar or police officer, but "[f]or the statistics, look no further. We can help. We can tell you exactly why robbing banks is a bad idea."

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This planet obeys the law—stats on volcanic eruptions show pattern called Benford’s Law

Scientists delight in extracting order from chaos—finding patterns in the complexity of the real world that pull back the curtain and reveal how things work. Sometimes, though, those patterns create more head-scratching than excitement. Such is the case with Benford’s law. One might expect a collection of real-world data—say, the half-lives of various isotopes, for example—to pretty much look like random numbers. And one might further expect the first (non-zero) digit of each of those numbers to also be random (i.e. just as many 2s as 9s).

Oddly, one would (in many cases) be wrong. It turns out that 1s are more likely than 2s, which are more likely than 3s, and so on. Not only that, the probabilities match a logarithmic distribution, just like the spacing on a logarithmic scale. The number 1 will be the first digit about 30 percent of the time, 2 will occur nearly 18 percent of the time, all the way on down to 9 showing up only about 5 percent of the time.

Law-abiding citizens everywhere will be happy to know our planet also obeys Benford's Law, with the duration and size of volcanic eruptions showing the same sort of pattern.

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Survival in academia, the tenure track not taken

Becoming a university professor requires a lot of work for very little financial reward, compared to most other professions. In STEM (science, technology, engineering, math) fields, the minimum requirement is four years of undergraduate education, plus anywhere between four and a half and eight years of graduate studies, followed by an (ever increasing) number of years of post-doctoral work. That may get you an assistant professorship where, at a state university, the starting salary is in the $60k-70k range. 

(The only other career path I have seen that has similarly low pay for exorbitant requirements is becoming a chef. In both cases, you only do them because you simply love doing them.)

The fortunate few who make it as assistant professors then end up busting their behinds in the hope of getting tenure. A new study published in last week's issue of Science, examined the rates of promotion to tenure at some major US universities. It found that there was no significant difference between the sexes when it came to promotion within an institution. But, in the process, it found that universities aren't doing so well with their investments in young faculty, as only half of their initial hires end up living out their career at the same institution.

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Linking correlation to causation with power laws and scale free systems

An essential part of science involves finding correlations between two sets of measurements and seeking explanations for those correlations. However, relationships can be suggested by data even when they don't actually exist, and correlations may occur due to random fluctuations rather than a deep underlying principle (as the infamous "correlation does not equal causation" cliché suggests). These errors are easy to make, and the scientific literature is full of them.

So how can researchers establish if a correlation is both real and meaningful? In a Perspective in the February 10 issue of Science, Michael P.H. Stumpf and Mason A. Porter examine the type of correlation known as a power law, where one set of measurements is related to a second via an exponent. They argue that two things must be in place for a power law to be valid as a predictive model: it must hold over a wide range of data to eliminate chance associations, and it must have a plausible mechanism to explain why the correlation showed up in the data.

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Linking correlation to causation with power laws and scale free systems

An essential part of science involves finding correlations between two sets of measurements and seeking explanations for those correlations. However, relationships can be suggested by data even when they don't actually exist, and correlations may occur due to random fluctuations rather than a deep underlying principle (as the infamous "correlation does not equal causation" cliché suggests). These errors are easy to make, and the scientific literature is full of them.

So how can researchers establish if a correlation is both real and meaningful? In a Perspective in the February 10 issue of Science, Michael P.H. Stumpf and Mason A. Porter examine the type of correlation known as a power law, where one set of measurements is related to a second via an exponent. They argue that two things must be in place for a power law to be valid as a predictive model: it must hold over a wide range of data to eliminate chance associations, and it must have a plausible mechanism to explain why the correlation showed up in the data.

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Cluster of >8.0-magnitude earthquakes doesn’t indicate Earth is more active

The past few years have seen an unusual number of epically large earthquakes, with several—in Sumatra, Chile, and Japan—reaching magnitudes of roughly 9.0. This has led a number of people to wonder whether large earthquakes cluster and, if they do, whether we should be getting nervous about when the next one will hit. A new analysis in PNAS, however, suggests the elevated activity is nothing unusual, although the long gap between recent activity and past monster quakes was statistically unlikely.

The authors went through the US Geological Survey's historic records, identifying every earthquake above magnitude 7.0 that occurred between 1900 and 2011. To eliminate aftershocks and local strain caused by initial earthquakes, the authors set a cutoff: any smaller earthquakes within three years and 1,000km of a quake were considered its aftershocks, and not incorporated into the analysis. This is a fairly liberal definition of aftershock, and takes two recent monster quakes out of the analysis, both over 8.5 and near the site of the first Sumatran quake. But it is consistent with what we know about how major quakes can add strain to areas at a considerable distance from where the fault actually ruptured.

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